Geometry and measures, Year 7: more practice

On the vertex (the corner) of the angle

HintIt goes where the two arms meet.

The whyThe baseline of the protractor must also lie along one arm, so the other arm points to the reading on the scale.

55° — read the other scale (180° − 125°)

HintAn acute angle is less than 90°.

The whyProtractors have two scales running in opposite directions. Start from 0° on the arm you are lined up with; 125° is the reading from the other end, and 180° − 125° = 55°.

Compasses, drawing two arcs

HintDraw the 7 cm base first, then you need two curves that cross.

The whyFrom one end of the base draw an arc of radius 5 cm, and from the other end an arc of radius 6 cm. They cross at the third vertex.

SAS (side, angle, side)

HintThe known corner sits between the two lengths.

The whySAS fixes one triangle only. The angle must lie between the two known sides; a given angle that is not between them can give two different triangles.

3

HintVolume is length × width × height, so work backwards by dividing.

The whyThe base area is 5 × 4 = 20 cm², and 60 ÷ 20 = 3. Check: 5 × 4 × 3 = 60.

No, it has none

HintImagine folding it along a diagonal or through the midpoints of opposite sides.

The whyFolding along a diagonal makes the two halves match in size but the corners do not land on each other. It does have rotational symmetry of order 2.

2

HintCount how many positions in a full turn look exactly the same.

The whyA rectangle fits onto itself after a half turn and after a full turn, so its order is 2.

(−3, 2)

HintThe y-axis is vertical: which way does the point move, and does its height change?

The whyThe image is the same distance from the mirror line on the other side, and 2 up as before. Reflecting in the y-axis changes the sign of x.

146

HintOne centimetre is split into ten small divisions on a ruler.

The why1 cm = 10 mm, so 14.6 × 10 = 146 mm. The 0.6 cm is six of the small divisions.

A chord

HintIt is not a radius or a diameter.

The whyA chord joins any two points on the circumference. The longest chord passes through the centre and is a diameter.